Note in a computer program a particular input always results in an identical output - unless you add randomness to the code - which is considered "pseudo-randomness" (due to it being technically deterministic)
No, you are considering computers 50 years old or more. This post and your previous post is false based on an intentional ignorance of contemporary computer science advance, Modern programing is no longer "linear"and Newtonian 100% deterministic, which after the the advances using fractal math and chaos models like AI programing, which can respond intelligently in human interactions You need to go beyond your assertions and provide references to support your argument. like the following.
Special Issue on Mathematical Modeling of Complex Systems: Fractals-Fractional-Itô-AI-DEs-Based Theories, Analyses and Applications
Mathematical modeling, geared towards describing different aspects of the real world, reciprocal interactions and dynamics thereof through mathematics, must be able to address universal concepts, which makes mathematical models unique as they, on their own, allow for the mechanization and automation of intellectual activity. The mathematical model based on specialized knowledge can be described as one which has a material pertaining to mathematical nature, and in the process of determining the properties of a model, there exists reliance on the rigor by which the different components are identified, formulated and arranged. The role of mathematical modeling and scientific computation becomes evident in processes such as analyzing, decision-making, solving practical problems, predicting and simulating, which requires the definition of which level of detail needs to be introduced in different parts of a mode as well as which simplifications need to be performed for facilitating its integration into different models that can simulate highly complex problems taking into account uncertainty.
Fractals as complex and infinitely detailed geometric shapes that are recursively defined having their small sections being similar to large ones are quintessentially used for describing different natural structures that adopt various degrees of self-similarity besides for designing some artificial structures. Fractal mathematics as an inspirational field reveals the underlying beauty of the universe whose whole is fractal in essence. Fractal geometry, in this landscape, as a mathematical tool provides lenses to comprehend complexity in systems and shapes towards the description of the chaotic, irregular and unpredictable. Differential equations (DEs), as exemplary units of analysis of dynamical systems as continuous and discrete time-evolution processes, on fractals pave the way to grasping exhaustive analysis foregrounding the construction of different mathematical models in complex settings. Differential equations can be employed to describe dynamic phenomena and model complex systems’ behaviors while facilitating the prediction of future behavior depending on how existing values are connected and change in relation to one another over time. In the fractal setting, differential and integral operators with fractional order and fractal dimensions are employed to mathematically model complex problems with high multiplicity encountered related to phenomena which are not possible to be modeled with classical and nonlocal differential and integral operators with single order. Fractional differential equations can be employed for modeling problems through the exploration of various definitions of fractional derivative and integrals with new methods on fractional analysis, theory and applications. Stochastic differential equations, on the other hand, are used to model complex real-world problems; and Itô calculus, extending the methods of calculus to stochastic processes, has significant application areas in stochastic differential equations and mathematics-related fields. The inclusion of fractional-order operators in this setting, with order being a parameter per se, enables a single fractional-order operator to interpolate between all the orders’ derivatives, which allows fitting a specified number of fractional derivatives to data. Fractional derivatives, on the other hand, provide a means to describe memory and hereditary related properties of different processes as well as materials.
Fractional Calculus (FC), introduced as the extension of classical derivative calculus, is used to replicate complex problems and to examine the dynamical and nonlinear aspects of mathematical models that arise in science and engineering. All in all, fractional calculus approach provides novel models with the introduction of fractional-order calculus to optimization methods with the aim of maximizing the model accuracy and minimizing computational burden and other functions. Although fractal mathematics may not directly be used to predict the big events in chaotic systems, it can suggest such events will happen, and in this setting, Artificial Intelligence (AI) reminds us that the world is complex while being amusingly unpredictable. Neural networks, equipped with self-learning and self-adaptive capabilities, as well as deep neural networks are capable of solving numerical aspects of partial differential equations are important applications in systems, providing a broad array of interfaces for the output of calculation results. The multiple layers of neural networks can approximate nonlinear continuous functions with arbitrary accuracy which enables applicability to solve problems that have inherent complex mechanisms. Fit into the neural network framework, differential equations with some parameters produce the solution as output to describe the behavior of complex systems, and thus, using differential equation models in neural networks enable the models to be combined with approaches related to neural networks. Consequently, differential/integral equations, fractals, multifractals, fractional calculus, Itô calculus, as well as machine learning methods such as AI, deep learning, data science, algorithms, probability and stochastic processes, data-driven modeling, quantization optimization algorithm, system identification, synchronization, control, power, convergence, bifurcation, chaos, sensitivity, stability, complexity and computing, among many others are worthy of further investigation. Thus, the importance of generating applicable solutions to problems for diverse realms in engineering, medicine, life sciences, environmental sciences, physics, mathematical science, applied mathematics, mathematical biology, biology, bioengineering, applied disciplines, computer science, data science, image / signal processing and scientific computing, social sciences, to name some, appears to be a compelling requirement. This kind of a unifying approach is believed to enable comprehensive understanding towards behavior related to a broad range of systems and how complex phenomena are at work spanning across extensive spectra.
In view of these aspects, our special issue aims to provide a way towards original multidisciplinary and goal-oriented research based on advanced mathematical modeling and computational foundations. Hence, we expect to receive submissions on theoretical, computational and applied dimensions, merging mathematical analyses, methods, simulations, experimental designs, case studies, analyses, reviews, computer-assisted translations, computing technologies, and so forth to be presented in order to demonstrate the significance of novel approaches and schemes in real systems as well as related realms.
Please respond with references?